Stopping Sets of Algebraic Geometry Codes over Hyperelliptic Curves of Genus Two

Abdulla Eid ()
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Abdulla Eid: Department of Mathematics, University of Bahrain, Sakhir Campus, Zallaq P.O. Box 32038, Bahrain

Mathematics, 2024, vol. 12, issue 22, 1-11

Abstract: Stopping sets are useful for analyzing the performance of a linear code under an iterative decoding algorithm over an erasure channel. In this paper, we consider stopping sets of one-point algebraic geometry codes defined by a hyperelliptic curve of genus g = 2 defined by the plane model y 2 = f ( x ) , where the degree of f ( x ) was 5. We completely classify the stopping sets of the one-point algebraic geometric codes C = C Ω ( D , m P ∞ ) defined by a hyperelliptic curve of genus 2 with m ≤ 4 . For m = 3 , we proved in detail that all sets S ⊆ { 1 , 2 , ⋯ , n } of a size greater than 3 are stopping sets and we give an example of sets of size 2 , 3 that are not.

Keywords: stopping sets; algebraic geometric codes; Riemann–Roch spaces; hyperelliptic curves (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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